The CMA-ES is one of the most powerful stochastic numerical optimizers to address difficult black-box problems. Its intrinsic time and space complexity is quadratic—limiting its applicability with increasing problem dimensionality. To circumvent this limitation, different large-scale variants of CMA-ES with subquadratic complexity have been proposed over the past ten years. To-date however, these variants have been tested and compared only in rather restrictive settings, due to the lack of a comprehensive large-scale testbed to assess their performance. In this context, we introduce a new large-scale testbed with dimension up to 640, implemented within the COCO benchmarking platform. We use this testbed to assess the performance of several promising variants of CMA-ES and the standard limited-memory L-BFGS. In all tested dimensions, the best CMA-ES variant solves more problems than L-BFGS for larger budgets while L-BFGS outperforms the best CMA-ES variant for smaller budgets. However, over all functions, the cumulative runtime distributions between L-BFGS and the best CMA-ES variants are close (less than a factor of 4 in high dimension). Our results illustrate different scaling behaviors of the methods, expose a few defects of the algorithms and reveal that for dimension larger than 80, LM-CMA solves more problems than VkD-CMA while in the cumulative runtime distribution over all functions the VkD-CMA dominates LM-CMA for budgets up to 104 times dimension and for all budgets up to dimension 80.
CITATION STYLE
Varelas, K., Auger, A., Brockhoff, D., Hansen, N., ElHara, O. A., Semet, Y., … Barbaresco, F. (2018). A comparative study of large-scale variants of CMA-ES. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11101 LNCS, pp. 3–15). Springer Verlag. https://doi.org/10.1007/978-3-319-99253-2_1
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